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          <h1 class="post-title" itemprop="name headline">【三】Python3入门机器学习经典算法与应用——最基础的分类算法-kNN近邻算法</h1>
        

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        <p>本文为慕课网《Python3入门机器学习经典算法与应用》的第四章，主要讲解：最基础的分类算法-kNN近邻算法<br>本课程视频地址：<a href="https://coding.imooc.com/class/169.html" target="_blank" rel="noopener">https://coding.imooc.com/class/169.html</a><br>本课程代码地址：<a href="https://gitee.com/aiolos123/machine-learning-classical-algorithm-with-python3" target="_blank" rel="noopener">https://gitee.com/aiolos123/machine-learning-classical-algorithm-with-python3</a><br>讲师代码地址：<a href="https://github.com/liuyubobobo/Play-with-Machine-Learning-Algorithms" target="_blank" rel="noopener">https://github.com/liuyubobobo/Play-with-Machine-Learning-Algorithms</a></p>
<a id="more"></a>

<h2 id="kNN-k-Nearest-Neighbors-算法-k近邻算法"><a href="#kNN-k-Nearest-Neighbors-算法-k近邻算法" class="headerlink" title="kNN(k-Nearest-Neighbors)算法 - k近邻算法"></a>kNN(k-Nearest-Neighbors)算法 - k近邻算法</h2><blockquote>
<p>k近邻算法的特点： 思想极度简单；应用数学知识少(近乎为0)；效果好；可以解释机器学习算法使用过程中的很多细节问题；更完整的刻画机器学习应用的流程；</p>
</blockquote>
<ol>
<li><p>k近邻算法的思想：<strong>根据 新来的数据点在特征空间中的距它最近的K个特征点的特征，决定新来的数据点的特征</strong><br><img src="/blog/images/20200111075620178.jpg" alt="k近邻算法的思想"></p>
</li>
<li><p>欧拉距离：计算两点间的距离的一种方法<br><img src="/blog/images/20200113060945647.jpg" alt="欧拉距离"></p>
</li>
<li><p>k近邻算法的代码实现(使用欧拉距离计算两点之间的距离)</p>
<figure class="highlight makefile"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line">from math import sqrt</span><br><span class="line">distances = []</span><br><span class="line">for x_train in X_train:</span><br><span class="line">    <span class="comment"># 计算样本数据与新数据的每个维度的欧拉距离</span></span><br><span class="line">    d = sqrt(np.sum((x_train - x)**2))</span><br><span class="line">    distances.append(d)</span><br><span class="line"><span class="comment"># 等价于 distances = [sqrt(np.sum((x_train - x)**2)) for x_train in X_train]</span></span><br><span class="line">nearest = np.argsort(distances) <span class="comment">#排序，返回索引</span></span><br><span class="line">k = 6</span><br><span class="line"><span class="comment"># 最近的k个点对应的y</span></span><br><span class="line">topK_y = [y_train[i] for i in nearest[:k]]</span><br><span class="line"><span class="comment"># 统计topK_y中不同标签的个数</span></span><br><span class="line">from collections import Counter</span><br><span class="line">votes = Counter(topK_y)</span><br><span class="line"></span><br><span class="line"><span class="comment"># 获取标签最多的元素</span></span><br><span class="line">votes.most_common(1)</span><br><span class="line"><span class="comment"># KNN预测结果</span></span><br><span class="line">predict_y = votes.most_common(1)[0][0]</span><br></pre></td></tr></table></figure>

</li>
</ol>
<h2 id="scikit-learn中的机器学习算法封装"><a href="#scikit-learn中的机器学习算法封装" class="headerlink" title="scikit-learn中的机器学习算法封装"></a>scikit-learn中的机器学习算法封装</h2><ol>
<li>将上述k近邻算法的代码实现过程封装为一个函数，代码如下<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> numpy <span class="keyword">as</span> np</span><br><span class="line"><span class="keyword">from</span> math <span class="keyword">import</span> sqrt</span><br><span class="line"><span class="keyword">from</span> collections <span class="keyword">import</span> Counter</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">kNN_classify</span><span class="params">(k, X_train,y_train, x)</span>:</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">assert</span> <span class="number">1</span> &lt;= k &lt;= X_train.shape[<span class="number">0</span>], <span class="string">"k must be valid"</span></span><br><span class="line">    <span class="keyword">assert</span> X_train.shape(<span class="number">0</span>) == y_train.shape[<span class="number">0</span>], \</span><br><span class="line">            <span class="string">"the size of X_train must equal to the size of y_train"</span></span><br><span class="line">    <span class="keyword">assert</span> X_train.shape(<span class="number">1</span>) == x.shape[<span class="number">0</span>], \</span><br><span class="line">            <span class="string">"the feature number of x must be equal to X_train"</span></span><br><span class="line"></span><br><span class="line">    distances = [sqrt(np.sum((x_train - x)**<span class="number">2</span>)) <span class="keyword">for</span> x_train <span class="keyword">in</span> X_train]</span><br><span class="line">    nearest = np.argsort(distances)</span><br><span class="line"></span><br><span class="line">    topK_y = [y_train[i] <span class="keyword">for</span> i <span class="keyword">in</span> nearest[:k]]</span><br><span class="line">    votes = Counter(topK_y)</span><br><span class="line"></span><br><span class="line">    <span class="keyword">return</span> votes.most_common(<span class="number">1</span>)[<span class="number">0</span>][<span class="number">0</span>]</span><br></pre></td></tr></table></figure>

</li>
</ol>
<p>该函数的使用如下图：<br><img src="/blog/images/20200113062431343.jpg" alt="该函数的使用"></p>
<p>KNN的实现过程图例：<br><img src="/blog/images/20200113062505198.jpg" alt="KNN的实现过程图例"></p>
<p>总结：<br><strong>1. K近邻算法是非常特殊的，可以被认为是没有模型的算法。 但为了和其他算法统一，可以认为训练数据集就是模型本身</strong></p>
<p><strong>2. 对于所有机器学习的算法，都是统一的先进行fit得到模型，再进行perdict(对于kNN来说，训练数据集就是模型)</strong></p>
<h3 id="使用scikit-learn中的kNN"><a href="#使用scikit-learn中的kNN" class="headerlink" title="使用scikit-learn中的kNN"></a>使用scikit-learn中的kNN</h3><ol>
<li>使用scikit-learn中的kNN是方式如下<figure class="highlight makefile"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line">from sklearn.neighbors import KNeighborsClassifier</span><br><span class="line"><span class="comment"># 创建实例</span></span><br><span class="line">kNN_classifier = KNeighborsClassifier(n_neighbors=6) <span class="comment">#指定k</span></span><br><span class="line"><span class="comment"># fit过程,得到模型</span></span><br><span class="line">kNN_classifier.fit(X_train,y_train)</span><br><span class="line"><span class="comment"># 新来数据,sklearn要求传入矩阵</span></span><br><span class="line">x = np.array([8.0934343545412,3.365745674423])</span><br><span class="line">X_predict = x.reshape(1,-1)</span><br><span class="line"><span class="comment"># 使用模型进行predict过程</span></span><br><span class="line">y_predict = kNN_classifier.predict(X_predict)</span><br><span class="line"><span class="comment"># 预测结果</span></span><br><span class="line">y_predict[0]</span><br></pre></td></tr></table></figure>

</li>
</ol>
<p><strong>注意：所有机器学习算法都是这个封装、调用和执行过程</strong></p>
<h3 id="自己仿写scikit-learn中的kNN实现过程"><a href="#自己仿写scikit-learn中的kNN实现过程" class="headerlink" title="自己仿写scikit-learn中的kNN实现过程"></a>自己仿写scikit-learn中的kNN实现过程</h3><p>KNN.py的代码如下：</p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># -*- coding: UTF-8 -*-</span></span><br><span class="line"><span class="keyword">import</span> numpy <span class="keyword">as</span> np</span><br><span class="line"><span class="keyword">from</span> math <span class="keyword">import</span> sqrt</span><br><span class="line"><span class="keyword">from</span> collections <span class="keyword">import</span> Counter</span><br><span class="line"></span><br><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">KNNClassifier</span>:</span></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">__init__</span><span class="params">(self, k)</span>:</span></span><br><span class="line">        <span class="string">"""初始化KNN分类器"""</span></span><br><span class="line">        <span class="keyword">assert</span> k &gt;= <span class="number">1</span>, <span class="string">"k must be valid"</span></span><br><span class="line">        self.k = k</span><br><span class="line">        self._X_train = <span class="literal">None</span>;  <span class="comment"># 初始化训练集</span></span><br><span class="line">        self._y_train = <span class="literal">None</span>;</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">fit</span><span class="params">(self, X_train, y_train)</span>:</span></span><br><span class="line">        <span class="string">"""根据训练数据集X_train和y_train训练kNN分类器模型(对于KNN而言，训练数据集就是模型)"""</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">assert</span> X_train.shape[<span class="number">0</span>] == y_train.shape[<span class="number">0</span>], \</span><br><span class="line">            <span class="string">"the size of X_train must equal to the size of y_train"</span></span><br><span class="line">        <span class="keyword">assert</span> self.k &lt;= X_train.shape[<span class="number">0</span>], \</span><br><span class="line">            <span class="string">"the size of X_train must be least k"</span></span><br><span class="line"></span><br><span class="line">        self._X_train = X_train</span><br><span class="line">        self._y_train = y_train</span><br><span class="line"></span><br><span class="line">        <span class="keyword">return</span> self  <span class="comment"># 返回函数自身</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">predict</span><span class="params">(self, X_predict)</span>:</span></span><br><span class="line">        <span class="string">"""给定待预测数据集X_predict, 返回表示X_predict的结果向量"""</span></span><br><span class="line">        <span class="keyword">assert</span> self._X_train <span class="keyword">is</span> <span class="keyword">not</span> <span class="literal">None</span> <span class="keyword">and</span> self._y_train <span class="keyword">is</span> <span class="keyword">not</span> <span class="literal">None</span>, \</span><br><span class="line">            <span class="string">"must fit before predict!"</span></span><br><span class="line">        <span class="keyword">assert</span> X_predict.shape[<span class="number">1</span>] == self._X_train.shape[<span class="number">1</span>], \</span><br><span class="line">            <span class="string">"the feature number of X_predict must be equal to X_train"</span></span><br><span class="line"></span><br><span class="line">        y_predict = [self._predict(x) <span class="keyword">for</span> x <span class="keyword">in</span> X_predict]</span><br><span class="line"></span><br><span class="line">        <span class="keyword">return</span> np.array(y_predict)</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">_predict</span><span class="params">(self, x)</span>:</span></span><br><span class="line">        <span class="string">"""给定单个待预测数据x，返回x的预测结果值"""</span></span><br><span class="line">        <span class="keyword">assert</span> x.shape[<span class="number">0</span>] == self._X_train.shape[<span class="number">1</span>], \</span><br><span class="line">            <span class="string">"the feature number of x must be equal to X_train"</span></span><br><span class="line"></span><br><span class="line">        <span class="comment"># 同kNN_classify()</span></span><br><span class="line">        distances = [sqrt(np.sum((x_train-x)**<span class="number">2</span>)) <span class="keyword">for</span> x_train <span class="keyword">in</span> self._X_train]</span><br><span class="line">        nearest = np.argsort(distances)</span><br><span class="line"></span><br><span class="line">        topK_y =[self._y_train[i] <span class="keyword">for</span> i <span class="keyword">in</span> nearest[:self.k]]</span><br><span class="line">        votes = Counter(topK_y)</span><br><span class="line"></span><br><span class="line">        <span class="keyword">return</span> votes.most_common(<span class="number">1</span>)[<span class="number">0</span>][<span class="number">0</span>]</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">__repr__</span><span class="params">(self)</span>:</span></span><br><span class="line">        <span class="keyword">return</span> <span class="string">"KNN(k=%d)"</span> % self.k</span><br></pre></td></tr></table></figure>

<p>调用过程如下：<br><img src="/blog/images/20200113110507507.jpg" alt="调用过程"></p>
<h2 id="判断机器学习的性能"><a href="#判断机器学习的性能" class="headerlink" title="判断机器学习的性能"></a>判断机器学习的性能</h2><p>4-3</p>

      
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            }
          }

          if ('auto' === 'auto') {
            input.addEventListener('input', inputEventFunction);
          } else {
            $('.search-icon').click(inputEventFunction);
            input.addEventListener('keypress', function (event) {
              if (event.keyCode === 13) {
                inputEventFunction();
              }
            });
          }

          // remove loading animation
          $(".local-search-pop-overlay").remove();
          $('body').css('overflow', '');

          proceedsearch();
        }
      });
    }

    // handle and trigger popup window;
    $('.popup-trigger').click(function(e) {
      e.stopPropagation();
      if (isfetched === false) {
        searchFunc(path, 'local-search-input', 'local-search-result');
      } else {
        proceedsearch();
      };
    });

    $('.popup-btn-close').click(onPopupClose);
    $('.popup').click(function(e){
      e.stopPropagation();
    });
    $(document).on('keyup', function (event) {
      var shouldDismissSearchPopup = event.which === 27 &&
        $('.search-popup').is(':visible');
      if (shouldDismissSearchPopup) {
        onPopupClose();
      }
    });
  </script>





  

  

  

  
  

  

  

  

</body>
</html>
